Method for the 3d modeling of a tubular structure

ABSTRACT

The invention provides a method for 3D modeling of a three-dimensional tubular structure of an examination object from 2D projection images (D) of the structure taken from different projection directions. The method has the following steps: reconstruction of a 3D image from the 2D projection images (D); selection of at least one 3D central line point (MO) in the 3D image, said 3D central line point being located in the structure; segmentation of 3D central line points (M) of the structure in the 3D image; forward projection of the 3D central line points (M), which have been segmented in the 3D image, into 2D projection images (D′); determination of border points of the structure in the 2D projection images (D′) on the basis of 3D central line points (Z) that have been projected in; and back-projection of the border points from the 2D projection image (D′) into the 3D image.

The present invention relates to a method for the 3D modeling of athree-dimensional tubular structure of an examination object from anumber of 2D projection images of the tubular structure taken fromdifferent projection directions. Furthermore, the invention relates to acorresponding 3D modeling device and also to a computer program forimplementing the method.

An accurate quantitative analysis of the coronary arteries is importantin order to diagnose ischemic disorders. The necessary user interactionis one limitation of the 3D modeling methods currently used, in whichthe central lines of the tubular vessel structures are defined in the 2Dprojection images. Such a method is described, for example, in “3DReconstruction of Coronary Arterial Treat to optimize AngiographicVisualation”, Chen S. and Carroll J., IEEE Trans. Medical Imaging,19:318-336 (2000). A method for the 3D modeling of a three-dimensionaltubular structure from 2D projection images is moreover also describedin European patent application 02 077 203.4 (ID 201823). In that case, a3D model of a tubular structure, for example the coronary vessels, isobtained from 2D projection images using so-called epipolar lines.

The automatic segmentation of the central lines of tubular structures iscurrently not possible on account of the superposition of the structuresin the 2D projection images and on account of the limited information ina projection. Furthermore, the 2D central lines currently have to beextracted from each projection independently of one another, and thisrequires a great number of complicated user interactions.

It is therefore an object of the invention to specify an improved methodfor the 3D modeling of a three-dimensional tubular structure of anexamination object, which method can be implemented with considerablyless user interaction and thus virtually automatically, with a highdegree of accuracy being achieved at the same time.

According to the invention, this object is achieved by a method asclaimed in claim 1, comprising the steps:

-   a) reconstruction of a 3D image from the 2D projection images,-   b) selection of at least one 3D central line point in the 3D image,    said 3D central line point being located in the tubular structure,-   c) segmentation of other 3D central line points of the tubular    structure in the 3D image,-   d) forward projection of the 3D central line points, which have been    segmented in the 3D image, into the 2D projection images,-   e) determination of border points of the tubular structure in the 2D    projection images on the basis of the 3D central line points that    have been projected in, and-   f) back-projection of the border points from the 2D projection    images into the 3D image.

This object is also achieved by a corresponding device, as specified inclaim 8. A computer program for implementing the method according to theinvention on a computer is specified in claim 9. Advantageous versionsof the invention are specified in the dependent claims.

The invention is based on the concept of determining information that isnecessary for the 3D modeling by a combination of the analysis of avolume reconstruction (which has a low resolution) of the 2D projectionson which it is based (which have a high resolution). The 3D central lineof the tubular structure that is to be modeled is in this casedetermined by segmenting the reconstructed volume data. In order toobtain the precise border points of the tubular structure, the 3Dcentral line points determined in the volume data are projected forwardinto the 2D projections on which they are based, and this has theadvantage that the correspondences between the 2D central line pointsresulting in the 2D projections are recognized automatically. The borderpoints of the tubular structure are then determined in the respective 2Dprojections, and these border points are then combined again byback-projection into the 3D volume in order to obtain a 3D estimate ofthe border points of the tubular structure. This information is thenused to create a 3D model of the tubular structure.

Compared to known methods, the method according to the inventionrequires hardly any user interaction; in principle, the method merelyrequires the selection of just one 3D central line point in the 3D imageas a start point for the segmentation of other 3D central line points.Moreover, the correspondences between the 3D central line pointsprojected into the 2D projection images are found automatically, so thatthere is no need for any complicated registering, for example by meansof epipolar lines as in the case of the method described in Europeanpatent application 02 077 203.4 (ID 210823). This means that the methodaccording to the invention also requires considerably less computationsteps while retaining the same high degree of accuracy.

The method according to the invention is independent of the imagingarchitecture used and can therefore for example process 2D projectionimages which have been taken using a monoplanar or biplanar X-raysystem, provided that the projection geometry, that is to say theposition of the detector plane and the focus point of the X-ray tubes,during taking of the 2D projection images is known. One potential fieldof application of medical imaging, in particular three-dimensionalrotation angiography, is the reconstruction of 2D images of objects thathave moved, such as the heart or coronary vessels of a patient forexample. The periodic movement of the object must be taken into accountin the imaging, which is why in one preferred version of the methodaccording to the invention a corresponding movement signal is used, saidmovement signal recording for example the contraction movement of theheart or the respiratory movement of the patient. A four-dimensionaldata set is thus recorded and reconstructed, with the time or theindividual movement phases of the periodic movement being used as thefourth dimension.

The method according to the invention is preferably used to image thecoronary vessels of a patient. The coronary vessels essentially undergoa periodic movement on account of the regular contraction of the heart.This movement is preferably recorded by means of an electrocardiogram(ECG), which is taken at the same time as the 2D projection images aretaken and thus makes it possible for the individual 2D projection imagesto be assigned to individual movement phases of the heart. As analternative or in addition, it is also possible, for example in otherapplications, such as an examination of a patient's lung, for arespiratory movement signal to be recorded, said respiratory movementsignal representing the respiratory movement of the patient while the 2Dprojection images are being taken. The respiratory movement is likewiseessentially a periodic movement, which can be taken into account andcompensated during reconstruction of the 4D image data set of thetubular structure in order to achieve an even higher degree of accuracy.In such applications, it is necessary that the 3D image reconstructedinitially from the 2D projection images has a low resolution since 2Dprojections that are not sufficient for reconstructing a 3D image havinga high resolution are present, for example in the same heart movementphase.

The method according to the invention can also be used for tubularstructures other than the coronary vessels, for example to reconstruct a4D image data set of the intestines or airways of a patient. However,the method according to the invention can be used not only in medicalimaging but also in principle in industrial imaging.

In a further preferred version of the method, in step b) at least onestart point and one end point of a 3D central line in the tubularstructure is selected, it also being possible for a number of 3D centralline points to be selected although this accordingly requires a greaternumber of user interactions. Nevertheless, a greater number of selected3D central line points increases the rapidity and accuracy of thesegmentation of other 3D central line points which is to be carried outin the next step.

In a further version, it is provided that the 3D image that is initiallyreconstructed from the 2D projection images is constructed with a lowresolution, as a result of which simpler and more rapid reconstructionis possible. The reconstruction of a 3D image from a two-dimensionaldata set, that is to say from 2D projection images taken at the samemovement phases within a periodic movement, is usually only possiblewith a low resolution, since data that are insufficient for a highresolution are present in the same movement phase. Nevertheless, themethod according to the invention makes it possible for a 3D model ofthe tubular structure to be created, since the determination of borderpoints of the tubular structure is carried out in the high-resolution 2Dprojection images.

In an advantageous further embodiment of the method according to theinvention, the determination of border points of the tubular structurein the 2D projection images takes place automatically, that is to saywithout user interactions. In this case, image values along a crosssection through the tubular structure are taken into account, and theprofile of the gray values in the cross section through the tubularstructure in a 2D projection image is thus considered, for example, withthe cross section being made through a 3D central line point projectedinto a 2D projection image. Using this gray value profile, it ispossible for the border points of the tubular structure to bedetermined, since at those points the image value or gray value profilehas an extremum. However, other possibilities are also known, such as,for example, methods based on the evaluation of the 1st or 2ndderivation of the image value or gray value profile or the so-calledscale space method which is known to the person skilled in the art.

The invention will be further described with reference to examples ofembodiments shown in the drawings to which, however, the invention isnot restricted.

FIG. 1 shows a flowchart of the method according to the invention and

FIG. 2 shows a pictorial representation of the essential method steps.

The essential steps of the method according to the invention are shownin the flowchart of FIG. 1. Into the 3D construction of a 3D image whichin this case has a low resolution, said 3D reconstruction taking placein the first step (1), there flow at least 2D projection data D whichhave been recorded for example using a CT scanner or C-arm X-ray devicefrom different viewing angles of the examination object, for example theheart of a patient. On account of the movement of the heart during therecording of the 2D projection data, only some of the 2D projections canbe used for the 3D volume reconstruction, with those that can be usedbelonging to the same movement phase of the heart. In order to filterout these 2D projections, ECG data E are recorded at the same time asthe 2D projection data are recorded. As a result, the number of usable2D projection data is of course reduced, which may result in disruptiveartifacts in the 3D image and only allows the creation of a 3D imagehaving low resolution. If, of course, an examination object which is notmoving is to be considered, the recording of the ECG data E or ingeneral the recording of a movement signal can be omitted, and allrecorded 2D projection data D can in principle be used for the 3Dreconstruction. An MIP image (MIP=Maximum Intensity Projection) is shownsymbolically for the reconstructed 3D image B in FIG. 2, in which MIPimage there can also be seen the tubular structure H that is to bemodeled, namely a number of vessels.

Whereas the image quality of the reconstructed (low-resolution) 3D imageis sufficient for an estimate of 3D central lines within tubularstructures in the 3D image, for example for estimating the 3D centrallines located within blood vessels when the coronary vessels are underconsideration, the resolution is not sufficient for a quantitativeanalysis of the border regions of the tubular structure H. In step 3,therefore, a segmentation of 3D central line points in the 3D image isfirst carried out after the user has selected (2) at least one startand/or end point M0 for the segmentation. For this purpose, there may beused, for example, a segmentation based on the so-called “frontpropagation method”, combined with a “propagation speed responsefunction” based on cylinder models, as described in “Vessel Segmentationfor Visualization of MRA with Blood Pool Contrast Agents”, Young S.,Pekar V. and Weese J., MICCAI 2001, Utracht, The Netherlands, 491-498.Other 3D central line segmentation methods can also be used for thispurpose, as described, for example, in O. Wink, W. J. Niessen and M. A.Viergever, “Minimum Cost Path Determination Using a Simple HeuristicFunction” in Proc. International Conference on Pattern Recognition—4,pp. 1010-1013, Barcelona, September 2000 or O. Wink, W. J. Niessen andM. A. Viergever, “Fast Delineation and Visualization of Vessels in 3DAngiographic Images,” in IEEE Transactions on Medical Imaging, Vol. 19,No. 4, pp. 337-346, April 2000. Examples of 3D central line points Mobtained for the vessels contained in the 3D image are shown in FIG. 2.

In the next step (4), the 3D central line points M obtained areprojected forward into the 2D projections D used initially toreconstruct the 3D image, as is likewise shown in FIG. 2 by way ofexample for two 2D projections D1′ and D2′. The projected-in 3D centralline points Z1, Z2 can also be seen therein. Since these central linepoints Z1, Z2 have been projected in from the same 3D volume, and sincethe projection geometry with which the respective 2D projection wastaken is known, the correspondences between the individual 3D centralline points Z1, Z2 between the individual 2D projections D1′, D2′ arefound automatically. There is thus no longer any need for a step toproduce these correspondences individually, for example by means ofcomplicated registering, for which purpose known methods use, forexample, the so-called epipolar line method.

Subsequently, the border points of the vessels H are then (5) determinedin each 2D projection D1′, D2′ on the basis of the central line pointsZ1, Z2. This may be effected, for example, using the gray value profilesin the 2D projections, since the gray value profile normally has anextremum at the borders of the vessels. This step is not shown in anygreater detail in FIG. 2.

The border points that have been found in the individual 2D projectionsD1′ are then (6) back-projected into the 3D image, with use again beingmade of the known correspondence of border points that are associatedwith one another on account of the known correspondence between thecentral line points Z1, Z2 and in the 2D projections D1′, D2′. Finally,a 3D model R, as shown in FIG. 2, of the vessel system can thus (7) bemodeled.

According to the invention, a 3D model of a tubular structure can thusbe created in a fully automatic manner, said 3D model having a highdegree of accuracy on account of the use of the high-resolution 2Dprojections to determine border points of the tubular structure. In theextreme, the user need select just one start point for the segmentationof the 3D central line points in the 3D volume. Where appropriate, eventhis selection can be fully automated. The method according to theinvention thus has a considerably lower computational complexity andrequires considerably less user interactions while retaining the samedegree of accuracy.

1. A method for the 3D modeling of a three-dimensional tubular structureof an examination object from a number of 2D projection images (D) ofthe tubular structure (H) taken from different projection directions,comprising the steps: a) reconstruction of a 3D image (B) from the 2Dprojection images (D), b) selection of at least one 3D central linepoint (M0) in the 3D image (B), said 3D central line point being locatedin the tubular structure (H), c) segmentation of other 3D central linepoints (M) of the tubular structure (H) in the 3D image (B), d) forwardprojection of the 3D central line points (M), which have been segmentedin the 3D image (B), into the 2D projection images (D′), e)determination of border points of the tubular structure (H) in the 2Dprojection images (D′) on the basis of 3D central line points (Z) thathave been projected in, and f) back-projection of the border points fromthe 2D projection images (D′) into the 3D image (B).
 2. A method asclaimed in claim 1, characterized in that in step b) at least one startpoint and one end point of a 3D central line (M) in the tubularstructure (H) is selected.
 3. A method as claimed in claim 1,characterized in that the 3D image (B) is reconstructed to have a lowresolution.
 4. A method as claimed in claim 1, characterized in that thedetermination of border points of the tubular structure (H) in the 2Dprojection images (D) in step e) takes place automatically, inparticular by taking account of the image values along a cross sectionthrough the tubular structure (H).
 5. A method as claimed in claim 1,characterized in that, in parallel with the taking of the 2D projectionimages (D), a movement signal (E) that represents a periodic movement ofthe examination object is recorded, and in that the 3D image (B) iscreated from 2D projection images (D) taken in the same movement phases.6. A method as claimed in claim 1, characterized in that anelectrocardiogram or a respiratory movement signal is used as movementsignal (E).
 7. A method as claimed in claim 1, characterized in that themethod is used to image the coronary vessels of a patient.
 8. A devicefor the 3D modeling of a three-dimensional tubular structure of anexamination object from a number of 2D projection images (D) of thetubular structure (H) taken from different projection directions,comprising: a) a reconstruction unit for reconstructing a 3D image (B)from the 2D projection images (D), b) selection means for selecting atleast one 3D central line point (M0) in the 3D image (B), said 3Dcentral line point being located in the tubular structure (H), c) asegmentation unit for segmenting other 3D central line points (M) of thetubular structure (H) in the 3D image (B), d) a forward projection unitfor the forward projection of the 3D central line points (M), which havebeen segmented in the 3D image (B), into the 2D projection images (D′),e) a border point determination unit for determining border points ofthe tubular structure (H) in the 2D projection images (D′) on the basisof the 3D central line points (Z) that have been projected in, and f) aback-projection unit for the back-projection of the border points fromthe 2D projection images (D′) into the 3D image (B).
 9. A computerprogram embodied in a computer-readable medium and having computerprogramming means for instructing a computer to carry out the steps ofthe method: a) reconstruction of a 3D image (B) from the 2D projectionimages (D), b) selection of at least one 3D central line point (M0) inthe 3D image (B), said 3D central line point being located in thetubular structure (H), c) segmentation of other 3D central line points(M) of the tubular structure (H) in the 3D image (B), d) forwardprojection of the 3D central line points (M), which have been segmentedin the 3D image (B), into the 2D projection images (D′), e)determination of border points of the tubular structure (H) in the 2Dprojection images (D′) on the basis of 3D central line points (Z) thathave been projected in, and f) back-projection of the border points fromthe 2D projection images (D′) into the 3D image (B).